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PH-EP-2015-153

(Submitted on 13 Jul 2015)

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Abstract

Observations of exotic structures in the $J/\psi p$ channel, that we refer to
as pentaquark-charmonium states, in $\Lambda_b^0\to J/\psi K^- p$ decays are
presented. The data sample corresponds to an integrated luminosity of 3/fb
acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude
analysis is performed on the three-body final-state that reproduces the
two-body mass and angular distributions. To obtain a satisfactory fit of the
structures seen in the $J/\psi p$ mass spectrum, it is necessary to include two
Breit-Wigner amplitudes that each describe a resonant state. The significance
of each of these resonances is more than 9 standard deviations. One has a mass
of $4380\pm 8\pm 29$ MeV and a width of $205\pm 18\pm 86$ MeV, while the second
is narrower, with a mass of $4449.8\pm 1.7\pm 2.5$ MeV and a width of $39\pm
5\pm 19$ MeV. The preferred $J^P$ assignments are of opposite parity, with one
state having spin 3/2 and the other 5/2.

Fit projections for (a) $m_{Kp}$ and (b) $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ for the reduced $\Lambda ^*$ model with two $P_c^+$ states (see Table 1). The data are shown as solid (black) squares, while the solid (red) points show the results of the fit. The solid (red) histogram shows the background distribution. The (blue) open squares with the shaded histogram represent the $P_c(4450)^+$ state, and the shaded histogram topped with (purple) filled squares represents the $P_c(4380)^+$ state. Each $\Lambda ^*$ component is also shown. The error bars on the points showing the fit results are due to simulation statistics.

Results for (a) $m_{Kp}$ and (b) $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ for the extended $\Lambda ^*$ model fit without $P_c^+$ states. The data are shown as (black) squares with error bars, while the (red) circles show the results of the fit. The error bars on the points showing the fit results are due to simulation statistics.

Various decay angular distributions for the fit with two $P_c^+$ states. The data are shown as (black) squares, while the (red) circles show the results of the fit. Each fit component is also shown. The angles are defined in the text.

$m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ in various intervals of $m_{Kp}$ for the fit with two $P_c^+$ states: (a) $m_{Kp}<1.55$ GeV, (b) $1.55<m_{Kp}<1.70$ GeV, (c) $1.70<m_{Kp}<2.00$ GeV, and (d) $m_{Kp}>2.00$ GeV. The data are shown as (black) squares with error bars, while the (red) circles show the results of the fit. The blue and purple histograms show the two $P_c^+$ states. See Fig. 7 for the legend.

Fitted values of the real and imaginary parts of the amplitudes for the baseline ($3/2^-$, $5/2^+$) fit for a) the $P_c(4450)^+$ state and b) the $P_c(4380)^+$ state, each divided into six $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ bins of equal width between $-\Gamma_0$ and $+\Gamma_0$ shown in the Argand diagrams as connected points with error bars ($m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ increases counterclockwise).
The solid (red) curves are the predictions
from the Breit-Wigner formula for the same mass ranges
with $M_0$ ($\Gamma_0$) of
4450 (39) $\mathrm{\,MeV}$ and 4380 (205) $\mathrm{\,MeV}$ , respectively,
with the phases and magnitudes at the resonance masses set to the
average values between the two points around $M_0$.
The phase convention sets $B_{0,\frac{1}{2}}=(1,0)$ for $\Lambda (1520)$. Systematic uncertainties are not included.

Projections onto $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K}$ in various intervals of $m_{Kp}$ for the reduced model fit (cFit) with two $P_c^+$ states of $J^P$ equal to $3/2^-$ and $5/2^+$: (a) $m_{Kp}<1.55$ GeV, (b) $1.55<m_{Kp}<1.70$ GeV, (c) $1.70<m_{Kp}<2.00$ GeV, (d) $m_{Kp}>2.00$ GeV, and (e) all $m_{Kp}$. The data are shown as (black) squares with error bars, while the (red) circles show the results of the fit. The individual resonances are given in the legend.

Various decay angular distributions for the fit with two $P_c^+$ states for $m(K^-p)>2$ GeV. The data are shown as (black) squares, while the (red) circles show the results of the fit. Each fit component is also shown. The angles are defined in the text.

Results from cFit for (a) $m_{Kp}$ and (b) $m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p}$ for the extended model with two $P_c^+$ states. The data are shown (black) squares with error bars, while the (red) circles show the results of the fit. Each $\Lambda ^*$ component is also shown. The (blue) open squares and (purple) solid squares show the two $P_c^+$ states.

Coordinate axes for the spin quantization of particle $A$ (bottom part),
chosen to be the helicity frame of $A$
($\hat{z}_{0}||\vec{p}_{A}$ in the rest frame of its mother particle or in the laboratory frame),
together with the polar ($\BA{\theta}{B}{A}$) and azimuthal ($\BA{\phi}{B}{A}$) angles
of the momentum of its daughter $B$ in the $A$ rest frame (top part).
Notice that the directions of these coordinate axes, denoted as
$\BA{\hat{x}}{0}{A}$,
$\BA{\hat{y}}{0}{A}$, and
$\BA{\hat{z}}{0}{A}$,
do not change when boosting from the helicity frame
of $A$ to its rest frame.
After the Euler
rotation ${\cal R}(\alpha=\BA{\phi}{B}{A},\beta=\BA{\theta}{B}{A},\gamma=0)$
(see the text),
the rotated $z$ axis, $\BA{\hat{z}}{2}{A}$,
is aligned with the $B$ momentum; thus the rotated coordinates
become the helicity frame of $B$.
If $B$ has a sequential decay, then the same boost-rotation process
is repeated to define the helicity frame for its daughters.

Parameterized dependence of (a) the relative signal efficiency and of (b) the background density
on the Dalitz plane. The units of the relative efficiency and of the relative background density are arbitrary.

Tables and captions

The $\Lambda ^*$ resonances used in the different fits. Parameters are taken from the PDG [14]. We take $5/2^-$ for the $J^P$ of the $\Lambda (2585)$.
The number of $LS$ couplings is also listed for both the "reduced" and "extended" models.
To fix overall phase and magnitude conventions, which otherwise are arbitrary, we set $B_{0,\frac{1}{2}}=(1,0)$ for $\Lambda (1520)$.
A zero entry means the state is excluded from the fit.

Summary of systematic uncertainties on $P_c^+$ masses, widths and fit fractions, and $\Lambda ^*$ fit fractions.
A fit fraction is the ratio of the phase space integrals of the matrix element squared for a single resonance and for the total amplitude.
The terms "low" and "high" correspond to the lower and higher mass $P_c^+$ states. The sFit/cFit difference is listed as a cross-check and not included as an uncertainty.